Symmetry and Asymmetry: The Method of Moving Spheres

Abstract

We consider some nonlinear elliptic equations on ${\mathbb{R}}^n$ and ${\mathbb{S}}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results. Moreover, by the global bifurcation theory, we obtain a multiplicity result for a class of semilinear elliptic equations.

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